Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.anqh)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=11/2, a₂>=11/2

For fixed z and a₁=11/2, a₂=11/2, b₁>=-11/2

For fixed z and a₁=11/2, a₂=11/2, b₁=3/2

http://functions.wolfram.com/07.25.03.anqh.01

Input Form

HypergeometricPFQ[{11/2, 11/2}, {3/2, 6}, z] == (1/(59535 z^3)) (32 E^(z/2) (-2520 + 1215 z - 378 z^2 + 1944 z^3 + 5280 z^4 + 3888 z^5 + 928 z^6 + 64 z^7) BesselI[0, z/2]) + (1/(59535 z^4)) (32 E^(z/2) (10080 - 4860 z + 1827 z^2 - 486 z^3 + 216 z^4 + 2592 z^5 + 3056 z^6 + 864 z^7 + 64 z^8) BesselI[1, z/2])

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]